A dynamical systems approach to speech processing

An approach to speech processing, based on nonlinear dynamical systems, is presented. It is shown that two fundamental problems in speech processing, dimensionality reduction and nonlinear temporal variability, can be addressed using geometrical methods from nonlinear dynamics. An effective dynamical system is extracted by training a nonlinear predictor of the signal samples. A variety of signal characteristics is then obtained from the properties of the resulting dynamical system such as the dimensionality and stability of its trajectories. The problem of time warping of speech is approached using a similar dynamical predictor, now acting directly on the acoustic features, provided that the magnitude of the time derivative of the feature vector is included in the predictor input. For the latter case the existence of a nonlinear predictor whose functional form is invariant with respect to nonlinear transformations of time is proven. The use of such dynamical predictors can replace or enhance existing methods for speech recognition